Exploratory cluster analysis

“Central to all of the goals of cluster analysis is the notion of the degree of similarity (or dissimilarity) between the individual objects being clustered.” (Elements of Statistical Learning)

SWS and JH Summaries

This exploratory analysis will only be run on the complete case data for JH and SWS subscales.

First, we can check the pairwise correlation between the scales. In the plot below, the upper triangles provide the pearson correlation values. The lower triangles show the bivariate scatter plots. The diagonal shows a simple histogram and density plot of the univariate scale data.

JH has the highest pairwise correlation with SWS strength (0.48. Several of the SWS subscales correlate at a moderate or high level with other SWS subscales. We will see the effect of this when we look at item-specific PCA and cluster analysis later.

PCA

We want to examine how the items cluster when an unsupervised approach is taken. To do so, we will run a PCA analysis of the items.

Because John Henryism is scored on a scale with a different range than SWS, we’ll center and scale each of the items before applying PCA.

The first principal component explains 17% of the overall variability. Every subsequent component explains less than 10% of the variability each. The inclusion of 7 principal components nearly covers 50% of overall variability. However, 28 are necessary to cover 90% of variability. The inclusion of other items or factors may be beneficial to improve the
PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11 PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22 PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30 PC31 PC32 PC33 PC34 PC35 PC36 PC37 PC38 PC39 PC40 PC41 PC42 PC43 PC44
Standard deviation 5.156 3.613 2.919 2.852 2.567 2.474 2.395 2.298 2.141 2.079 2.013 1.959 1.915 1.879 1.830 1.793 1.745 1.691 1.656 1.569 1.539 1.504 1.466 1.461 1.417 1.331 1.305 1.276 1.219 1.186 1.169 1.148 1.072 1.060 1.023 1.014 0.943 0.933 0.887 0.844 0.821 0.802 0.719 0
Proportion of Variance 0.174 0.085 0.056 0.053 0.043 0.040 0.038 0.035 0.030 0.028 0.027 0.025 0.024 0.023 0.022 0.021 0.020 0.019 0.018 0.016 0.016 0.015 0.014 0.014 0.013 0.012 0.011 0.011 0.010 0.009 0.009 0.009 0.008 0.007 0.007 0.007 0.006 0.006 0.005 0.005 0.004 0.004 0.003 0
Cumulative Proportion 0.174 0.260 0.315 0.369 0.412 0.452 0.489 0.524 0.554 0.582 0.609 0.634 0.658 0.681 0.703 0.724 0.744 0.763 0.781 0.797 0.812 0.827 0.841 0.855 0.868 0.880 0.891 0.902 0.911 0.921 0.930 0.938 0.946 0.953 0.960 0.967 0.972 0.978 0.983 0.988 0.992 0.997 1.000 1

2-Dimensional

Note that the first principle component (x-axis) nearly completely separates the John Henryism items from the SWS items. Some of the SWS strength items do tend to cluster with the JH items, when compressed to two dimensions.

The addition of a second principle component (y-axis) shows somewhat distinct clustering of SWS subscales.

3-Dimensional

K-Means Clustering

Before I could begin with my cluster analysis, I build a pairwise distance matrix based on the centered and standardized data.

Next, I complete a k-means clustering, where \(k=6\), which is the number of scales we expect to observe.

For the k-means clustering, it does appear that JH separates out cleanly, but SWS is a bit more difficult to separate out.

Cluster membership based on k-means clustering compared to expected scale.
Item assigned.cluster scale
SWS5 1 SWS emotion
SWS6
SWS7
SWS8
SWS9
SWS10
SWS30
SWS11 2 SWS vulnerable
SWS12
SWS13
SWS14
SWS15
SWS21 3 SWS care
SWS22
SWS23
SWS24
SWS25
SWS34
SWS1 4 SWS strength
SWS2
SWS3
SWS4
JH_1 JH
JH_2
JH_3
JH_4
JH_5
JH_6
JH_7
JH_8
JH_9
JH_10
JH_11
JH_12
SWS16 5 SWS vulnerable
SWS31
SWS17 SWS succeed
SWS18
SWS32
SWS33
SWS29 6 SWS strength
SWS35
SWS19 SWS succeed
SWS20

“Intuitively, the larger the silhouette widths, the better the clustering. Specifically, observations with large silhouette widths (almost one) are well clustered, those with silhouette widths around zero tend to lie between clusters, and those with negative silhouette widths are likely placed in the wrong cluster.” (Sandrine Dudoit’s PH C240C/STAT C245C course notes)

Cluster membership based on PAM (k=6) clustering compared to expected scale.
Item assigned.cluster scale
SWS1 1 SWS strength
SWS2 SWS strength
SWS3 SWS strength
SWS4 SWS strength
SWS29 2 SWS strength
SWS16 SWS vulnerable
SWS17 SWS succeed
SWS18 SWS succeed
SWS32 SWS succeed
SWS33 SWS succeed
JH_10 JH
SWS35 3 SWS strength
SWS19 SWS succeed
SWS20 SWS succeed
SWS21 SWS care
SWS22 SWS care
SWS23 SWS care
SWS24 SWS care
SWS25 SWS care
SWS34 SWS care
SWS5 4 SWS emotion
SWS6 SWS emotion
SWS7 SWS emotion
SWS8 SWS emotion
SWS9 SWS emotion
SWS10 SWS emotion
SWS30 SWS emotion
SWS11 5 SWS vulnerable
SWS12 SWS vulnerable
SWS13 SWS vulnerable
SWS14 SWS vulnerable
SWS15 SWS vulnerable
SWS31 SWS vulnerable
JH_1 6 JH
JH_2 JH
JH_3 JH
JH_4 JH
JH_5 JH
JH_6 JH
JH_7 JH
JH_8 JH
JH_9 JH
JH_11 JH
JH_12 JH
One approach is to pick the k that maximizes the silhouette width

One approach is to pick the k that maximizes the silhouette width

K-Modes

K-modes is a more appropriate clustering method for use when the data is categorical.

Finding 2 clusters

Items in cluster 1.
item cluster scale
JH_1 1 JH
JH_2 1 JH
JH_3 1 JH
JH_4 1 JH
JH_5 1 JH
JH_6 1 JH
JH_7 1 JH
JH_8 1 JH
JH_9 1 JH
JH_10 1 JH
JH_11 1 JH
JH_12 1 JH
SWS1 1 SWS strength
SWS2 1 SWS strength
SWS3 1 SWS strength
SWS4 1 SWS strength
Items in cluster 2.
item cluster scale
SWS21 2 SWS care
SWS22 2 SWS care
SWS23 2 SWS care
SWS24 2 SWS care
SWS25 2 SWS care
SWS34 2 SWS care
SWS5 2 SWS emotion
SWS6 2 SWS emotion
SWS7 2 SWS emotion
SWS8 2 SWS emotion
SWS9 2 SWS emotion
SWS10 2 SWS emotion
SWS30 2 SWS emotion
SWS29 2 SWS strength
SWS35 2 SWS strength
SWS17 2 SWS succeed
SWS18 2 SWS succeed
SWS19 2 SWS succeed
SWS20 2 SWS succeed
SWS32 2 SWS succeed
SWS33 2 SWS succeed
SWS11 2 SWS vulnerable
SWS12 2 SWS vulnerable
SWS13 2 SWS vulnerable
SWS14 2 SWS vulnerable
SWS15 2 SWS vulnerable
SWS16 2 SWS vulnerable
SWS31 2 SWS vulnerable

Finding 6 clusters

Items in cluster 1.
item cluster scale
SWS5 1 SWS emotion
SWS1 1 SWS strength
SWS2 1 SWS strength
SWS3 1 SWS strength
SWS4 1 SWS strength
SWS29 1 SWS strength
SWS35 1 SWS strength
SWS17 1 SWS succeed
SWS18 1 SWS succeed
SWS20 1 SWS succeed
SWS32 1 SWS succeed
SWS16 1 SWS vulnerable
SWS31 1 SWS vulnerable
Items in cluster 2.
item cluster scale
JH_12 2 JH
Items in cluster 3.
item cluster scale
SWS21 3 SWS care
SWS22 3 SWS care
SWS23 3 SWS care
SWS24 3 SWS care
SWS25 3 SWS care
SWS34 3 SWS care
SWS19 3 SWS succeed
SWS33 3 SWS succeed
Items in cluster 4.
item cluster scale
JH_1 4 JH
JH_2 4 JH
JH_3 4 JH
JH_5 4 JH
JH_6 4 JH
Items in cluster 5.
item cluster scale
SWS6 5 SWS emotion
SWS7 5 SWS emotion
SWS8 5 SWS emotion
SWS9 5 SWS emotion
SWS10 5 SWS emotion
SWS30 5 SWS emotion
SWS11 5 SWS vulnerable
SWS12 5 SWS vulnerable
SWS13 5 SWS vulnerable
SWS14 5 SWS vulnerable
SWS15 5 SWS vulnerable
Items in cluster 6.
item cluster scale
JH_4 6 JH
JH_7 6 JH
JH_8 6 JH
JH_9 6 JH
JH_10 6 JH
JH_11 6 JH

Impurity

Gini impurity: the measure of impurity in a node. 0 or 1 is best. 0.5 is worst.

\[I_G(n) = 1 - \sum_{i=1}^J (p_i)^2\]

where \(J\) is the number of classes present in the node and \(p\) is the distribution of the class in the node.

## [1] 1
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impurity n
0.0000000 41
0.1363636 43
0.3343109 1
0.3409091 3
0.3471074 11
0.3529412 1

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.2435  0.3513  0.3878  0.3867  0.4193  0.5363

## # A tibble: 2 x 2
##   impurity     n
##      <dbl> <int>
## 1    0        98
## 2    0.136     2

Appendix

Full PCA Results

item scale PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11 PC12 PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22 PC23 PC24 PC25 PC26 PC27 PC28 PC29 PC30 PC31 PC32 PC33 PC34 PC35 PC36 PC37 PC38 PC39 PC40 PC41 PC42 PC43 PC44
SWS1 SWS strength -6.2 0.9 -7.9 1.5 -2.9 1.0 -1.1 1.5 -1.9 0.1 1.4 -1.1 2.0 -0.2 -0.8 -1.7 0.2 0.3 0.2 -1.4 -0.6 0.0 0.8 1.4 1.2 -0.1 -0.4 -1.2 0.4 1.0 0.2 0.8 -2.5 -0.1 0.7 1.4 0.6 0.7 0.0 -1.3 2.3 0.2 -1.2 0
SWS2 -6.5 0.8 -4.4 -0.6 -2.7 -0.3 -2.2 0.7 -0.1 0.9 -2.0 -0.7 3.4 -0.5 -0.1 -0.2 -1.5 -0.8 -1.4 0.6 1.2 -3.4 -1.7 0.3 -0.8 1.2 2.5 1.0 0.0 -0.9 0.9 -2.1 1.9 0.0 -0.8 -0.3 -1.7 1.3 0.3 -1.3 -0.4 -0.5 0.3 0
SWS3 -4.7 -0.6 -8.2 1.5 -1.8 1.3 3.1 -2.0 2.9 -0.4 1.3 0.4 -0.4 0.0 1.4 2.2 -1.1 1.5 -1.2 0.4 1.7 0.8 0.1 -1.8 -2.6 -0.9 0.5 -2.5 -0.3 1.5 1.1 1.2 1.0 0.7 1.1 -1.2 -0.3 -0.6 0.6 1.5 -0.5 0.2 -0.4 0
SWS4 -5.8 -0.2 -6.0 4.0 -3.5 0.9 -0.5 1.9 -1.5 -2.4 -0.2 1.4 0.5 -0.3 0.5 -1.5 2.5 -0.8 0.6 -1.1 0.1 0.0 0.1 0.4 0.3 0.5 -2.1 1.2 -1.3 -2.3 -0.9 0.0 -0.7 -0.3 0.0 0.8 0.5 -1.3 -0.5 0.9 -2.2 -0.3 1.5 0
SWS29 -0.6 3.0 -3.5 -1.5 8.8 1.3 3.1 2.2 0.7 -1.2 3.0 -3.3 1.1 0.7 -0.3 -0.5 -2.2 -0.7 1.4 -1.7 0.5 0.3 1.6 -2.5 1.4 -1.5 0.2 1.4 -1.9 -1.2 0.5 -1.2 0.7 -0.1 -1.2 0.5 -0.1 0.1 -0.4 0.5 0.3 0.3 -0.2 0
SWS35 0.1 5.2 -2.8 -0.3 2.7 -0.4 1.1 0.7 1.8 -0.3 -1.6 -1.4 1.3 -3.7 -1.7 0.7 0.4 -3.0 3.5 1.4 -0.2 1.3 -3.0 1.3 -1.2 0.4 -1.3 2.4 2.0 1.5 -1.1 1.1 0.9 -0.6 0.5 -0.8 0.9 -0.3 1.1 -0.1 0.2 0.4 0.0 0
SWS5 SWS emotion 0.1 -5.1 -1.6 3.7 0.5 -2.9 -4.4 -2.3 3.7 2.0 3.5 0.8 1.1 2.4 0.5 1.3 -1.0 0.5 0.6 0.6 -2.5 0.3 1.5 -0.2 1.2 0.9 0.0 0.9 1.6 -0.4 -0.6 -1.1 1.4 -2.3 1.7 -0.3 0.0 -0.9 -0.8 -0.1 0.6 1.0 0.6 0
SWS6 3.3 -8.1 -1.3 2.7 1.1 -2.7 -3.0 1.1 1.4 1.3 0.2 0.6 1.2 1.2 0.2 0.7 1.0 -0.4 0.6 3.5 1.0 2.2 -1.3 0.9 0.6 0.6 -0.8 -0.7 -1.5 0.2 1.4 0.1 -0.2 -0.2 -3.6 0.4 0.8 0.1 0.7 0.7 0.2 -0.9 -0.9 0
SWS7 5.0 -3.7 -0.3 0.2 4.1 -0.3 6.4 0.7 -1.2 -3.2 0.4 4.3 1.7 0.7 0.1 2.2 2.0 -0.6 -2.9 -2.6 -1.7 -2.2 -0.2 1.4 0.1 2.5 0.5 -0.1 0.7 1.2 0.2 0.8 0.9 -0.9 -0.5 0.6 0.4 -0.2 -0.2 -0.3 -0.1 -0.4 -0.5 0
SWS8 6.6 -6.1 0.7 1.9 0.3 -1.4 1.2 1.7 -0.9 -0.5 -1.5 0.2 -0.1 -2.8 1.1 -0.2 -0.4 0.1 1.1 0.8 2.5 -1.1 1.0 -2.1 -2.7 0.8 0.2 1.2 0.1 -1.6 1.4 0.9 -0.7 1.0 0.8 -1.0 1.1 -0.5 -1.8 -0.7 2.0 -0.5 0.9 0
SWS9 5.9 -6.7 1.3 1.7 1.1 -2.7 0.6 1.5 -1.2 0.3 -1.0 0.1 0.8 -0.5 -0.5 -0.3 0.1 1.3 1.8 0.4 0.9 -2.7 0.3 0.0 -1.7 -2.2 -0.4 -0.7 -0.3 -1.1 -2.0 1.0 -0.4 -0.3 0.4 1.1 -1.3 0.9 1.3 -0.1 -1.0 2.5 -0.9 0
SWS10 6.4 -6.5 0.3 1.7 -0.5 -1.1 1.4 0.7 -4.2 -0.9 -0.7 -0.2 1.2 -0.7 -1.3 -1.7 -0.5 0.5 1.7 -1.4 -0.6 1.7 -2.2 0.0 3.1 -1.9 1.7 -0.9 0.6 0.1 0.7 -1.7 0.2 0.0 2.3 -1.5 -0.1 0.4 0.9 1.0 -0.3 -1.4 0.1 0
SWS30 6.1 -2.3 -0.6 3.2 2.2 -0.6 -1.1 2.0 0.9 0.6 -0.5 -2.7 -1.5 -0.9 -0.6 0.1 -1.1 -1.4 -3.5 0.5 -2.6 1.5 1.1 -1.6 -0.7 0.1 -2.9 -0.1 0.1 1.8 0.2 -0.1 -0.4 1.4 0.9 0.8 -1.4 1.0 0.1 -1.6 -1.3 -1.1 0.6 0
SWS11 SWS vulnerable 5.4 -3.2 -1.1 -2.6 -3.3 2.7 0.3 -2.4 1.4 -2.4 -2.3 -1.7 -0.5 -2.4 -2.1 -3.1 -1.8 2.9 1.2 0.2 -4.7 0.3 1.1 0.9 -1.1 0.3 1.7 0.2 -0.8 0.9 -0.4 -0.2 1.0 0.8 -1.7 0.8 0.4 -1.0 -0.7 0.3 0.0 0.5 0.1 0
SWS12 4.3 -0.3 0.1 -4.1 2.4 3.9 -1.4 -0.6 3.2 -0.9 -4.2 -0.2 4.1 0.8 3.8 -0.6 -2.0 2.8 -2.3 0.6 1.5 -0.4 -0.2 0.0 1.8 0.4 -1.2 0.2 0.6 0.2 -1.9 -0.3 -2.3 -0.5 0.3 -1.1 0.4 -0.5 0.3 0.2 -0.2 -0.2 0.1 0
SWS13 6.2 -1.3 -0.9 -3.1 -5.1 0.2 1.6 0.5 2.0 0.2 1.6 -1.6 -2.3 2.2 -0.6 1.0 1.1 -2.8 1.0 0.6 0.5 -0.9 -1.5 -2.5 0.8 0.0 1.5 0.7 0.4 0.4 -2.8 0.5 -1.1 -0.6 -0.3 0.1 -0.9 -0.2 -2.0 0.1 -0.4 -1.1 -1.3 0
SWS14 6.5 -1.5 -0.4 -4.2 -3.3 2.3 0.6 -0.3 2.9 0.8 0.6 -0.5 -3.2 1.5 -1.0 0.6 1.5 -1.2 0.7 -2.0 -0.3 -1.4 -0.7 -1.9 1.0 1.4 -0.5 0.0 -0.3 -0.5 2.3 -0.7 -1.2 -0.1 -0.4 -0.5 0.7 0.0 2.8 -0.7 0.3 1.2 1.0 0
SWS15 6.1 -0.7 -0.7 -3.2 -2.2 0.6 1.7 -3.2 0.7 1.0 -0.8 -2.8 -1.6 1.6 1.5 0.6 0.5 1.2 0.5 -1.5 2.2 0.1 0.0 4.2 1.0 -1.3 -3.1 0.8 0.0 -1.0 1.5 1.0 2.3 -0.1 0.5 0.8 -0.8 0.7 -1.0 -0.1 0.3 -0.4 0.0 0
SWS16 1.9 1.0 -0.3 -3.7 -0.8 -1.9 -3.6 4.7 -1.1 1.2 0.5 0.6 -2.1 0.6 2.6 -0.5 0.6 0.5 0.9 -1.6 1.3 -0.6 3.2 0.5 -1.4 0.3 0.8 0.5 -0.6 2.4 -2.1 -0.6 1.6 0.0 0.4 0.5 1.6 1.0 1.2 0.9 0.2 -1.1 0.4 0
SWS31 2.9 1.5 0.0 -4.5 1.1 -0.1 -3.8 -1.1 -0.1 -0.6 -1.3 0.8 2.0 1.6 -2.1 -3.3 1.4 -5.2 -2.7 0.2 -0.5 -0.2 1.8 0.0 -1.3 -2.8 0.4 -1.9 0.9 -1.0 1.1 1.4 0.5 -0.9 0.0 -0.9 0.8 0.0 -0.5 0.5 -0.2 0.2 0.0 0
SWS17 SWS succeed 1.1 0.9 -0.8 -4.3 2.6 -0.3 -2.8 1.0 1.6 -4.7 3.1 2.6 -3.2 -4.0 2.2 -0.1 -0.2 -0.8 0.9 0.8 1.0 1.2 -1.3 1.6 0.9 1.0 0.6 -3.3 0.8 -1.0 -0.4 -1.1 -0.2 0.6 0.1 0.4 -1.0 0.5 -0.8 -0.6 -0.1 0.6 0.4 0
SWS18 -0.4 2.4 -0.5 -2.5 0.1 -1.5 -3.5 0.1 -2.3 0.2 0.3 1.7 -0.9 -1.8 2.6 5.0 -0.3 0.0 0.0 0.6 -3.3 -1.9 -0.4 1.0 0.9 -2.9 0.5 2.2 -2.3 0.6 1.5 0.9 -1.3 0.4 0.2 -1.2 -0.1 -0.3 -0.5 0.1 -0.3 0.2 -0.3 0
SWS19 4.5 3.0 -0.6 1.1 0.3 -2.7 3.2 -4.2 -1.0 4.8 0.0 0.1 1.1 -0.8 3.0 -2.1 1.9 -1.3 -1.1 0.3 1.5 2.4 -0.2 0.1 1.5 0.1 2.9 0.4 -1.4 1.5 -0.4 0.4 -0.4 0.6 -0.1 0.9 0.5 0.1 -0.5 -0.9 -0.6 1.4 1.1 0
SWS20 2.3 4.8 0.5 -0.3 0.5 -4.6 0.5 -5.3 -1.8 1.7 2.8 -0.9 -0.7 -3.5 0.8 -2.9 0.2 0.2 -1.5 1.0 -0.7 -2.4 0.8 -0.5 0.1 2.0 -1.4 0.1 0.0 -1.6 -0.4 -0.5 -0.3 0.3 0.2 -0.1 -0.5 -1.1 1.4 1.2 0.4 -1.1 -1.2 0
SWS32 1.2 2.5 -0.2 -1.5 2.5 -0.1 -1.8 -1.3 -1.3 5.0 -2.7 2.1 0.9 1.6 -2.8 2.1 -1.4 -0.4 2.3 -3.3 -0.6 0.8 -1.4 0.2 -1.7 1.7 -1.1 -2.7 -2.4 -0.6 -1.4 -0.5 -0.2 0.7 0.2 -0.4 -0.6 -0.9 -0.7 -0.2 0.4 -0.3 0.1 0
SWS33 1.4 3.0 -2.7 -2.4 1.8 -3.3 -2.4 -2.8 -4.7 -2.3 1.5 0.9 -2.0 3.0 -4.6 0.2 -1.8 4.1 -0.9 0.9 2.2 0.2 -1.0 -1.0 0.0 0.2 0.0 1.2 1.5 0.7 -0.1 1.2 -0.5 -0.1 -0.8 -0.1 0.6 0.2 -0.2 -0.7 -0.7 0.1 0.7 0
SWS21 SWS care 3.3 5.7 1.2 2.1 -1.7 0.6 2.9 -1.0 0.5 0.5 0.6 3.3 -0.5 0.9 1.9 -1.5 -1.4 1.0 0.7 -0.2 -1.8 1.4 -1.1 -0.3 -3.5 -0.9 -0.8 0.6 0.5 -0.6 0.9 -2.0 -1.5 -2.2 -0.5 0.1 0.4 2.7 -0.6 0.5 -0.1 -0.2 -0.1 0
SWS22 3.1 5.0 3.3 3.9 -1.5 2.2 -1.2 0.5 1.5 -0.2 2.2 4.3 2.1 1.7 1.9 -1.8 -0.5 0.7 2.7 -1.2 0.0 -0.2 0.1 -1.1 0.6 -1.9 -0.1 0.3 1.7 0.0 0.2 1.5 1.1 2.2 -1.1 0.1 -0.8 -1.3 0.8 -1.5 -0.1 -0.9 -0.3 0
SWS23 4.2 6.2 3.4 3.6 -1.0 1.0 -1.0 2.2 0.2 -0.9 -0.3 -2.4 -0.4 -0.5 -0.6 0.7 0.7 1.6 -0.2 0.8 1.2 -0.6 0.1 -0.1 0.3 0.6 0.0 -1.6 -1.3 0.0 1.1 -1.4 1.1 -1.1 1.0 -0.5 2.4 -1.0 -0.7 -1.6 -1.5 0.5 -1.6 0
SWS24 3.3 6.4 2.2 5.3 -0.4 0.7 -0.1 2.5 1.4 0.2 0.6 -1.2 0.6 -0.9 -2.4 -0.5 2.6 1.7 -0.2 0.7 0.0 -2.4 0.3 0.3 1.9 0.5 -0.4 -1.5 -0.7 1.4 -0.2 1.1 0.1 -0.5 -1.0 -1.8 -1.4 1.3 -0.9 1.5 1.0 0.4 1.4 0
SWS25 4.4 3.7 0.7 2.3 -1.2 1.0 1.8 3.8 -3.0 -0.7 0.8 -3.3 -1.2 3.4 1.4 1.6 -1.6 -0.6 -2.1 1.5 -1.0 2.4 0.3 3.0 -1.6 0.5 2.0 -0.1 0.4 -2.2 -1.0 0.4 -0.4 0.0 -0.3 -0.8 -0.9 -1.3 1.2 0.0 0.9 0.3 0.4 0
SWS34 4.6 4.6 1.8 2.2 -0.9 2.2 -1.8 -0.8 0.7 -2.0 -3.2 2.7 0.3 0.3 -2.6 2.4 -0.3 -1.2 -0.7 1.7 1.5 0.7 0.8 -0.7 0.9 0.5 0.9 1.3 -0.2 0.0 1.0 -1.0 -0.1 0.9 1.6 3.4 -0.6 -0.1 0.3 1.7 0.8 0.3 -0.3 0
JH_1 JH -7.4 -1.5 4.7 -1.1 -3.9 -1.1 2.7 -0.6 -2.6 -3.0 1.0 0.5 1.3 2.4 1.1 -0.9 -4.5 -3.2 0.4 2.0 -0.2 -0.6 -0.5 -0.6 1.2 1.1 -2.6 -0.5 -1.7 1.4 -0.6 -0.1 1.0 1.1 0.2 -0.6 0.8 0.6 -0.2 0.2 0.5 1.1 0.2 0
JH_2 -8.3 -0.6 2.3 -0.8 -0.9 -2.2 1.3 -1.0 0.8 -2.7 -3.1 1.9 -1.6 -0.9 -0.9 -1.0 0.8 0.1 0.7 -0.4 1.3 2.6 3.1 -0.3 0.2 -0.1 0.1 0.9 -1.8 0.8 0.1 0.1 -0.2 -2.7 -0.1 -1.3 -2.3 -0.8 0.8 -1.3 0.4 -0.4 -0.4 0
JH_3 -7.8 0.5 2.1 0.2 0.7 -3.6 1.9 -1.5 5.0 -1.2 -0.3 -0.5 0.8 1.4 -2.1 1.4 0.7 0.7 1.0 0.0 -1.0 0.5 1.9 1.5 0.6 0.8 1.6 0.3 -0.3 -2.3 -0.6 1.2 -0.9 2.3 0.9 -0.7 1.3 2.2 0.3 -0.3 -0.8 -0.8 -0.2 0
JH_4 -6.9 -0.2 2.8 1.4 -0.8 -4.4 1.7 -1.4 2.2 -1.4 -0.5 -1.7 -0.3 -0.3 -0.8 1.9 1.4 0.2 -2.0 -1.3 0.7 -1.0 -1.4 0.4 -0.9 -3.9 -0.6 -0.9 0.9 0.7 -1.3 -2.9 -0.5 0.6 -1.1 1.0 0.8 -1.4 0.0 -0.2 1.1 -0.3 0.8 0
JH_5 -5.3 0.1 1.8 -2.1 -1.5 -3.5 1.1 4.5 -0.2 3.3 -1.4 -0.1 -0.2 -0.7 -0.2 -0.1 -1.7 -0.1 0.2 -2.0 0.5 0.7 1.6 0.6 0.7 1.3 -0.3 0.4 3.4 0.6 2.0 -0.7 -1.1 1.0 -1.0 -0.4 -0.6 -0.9 -1.1 1.3 -1.2 1.2 -0.7 0
JH_6 -8.0 0.6 3.8 -2.4 -0.3 -1.0 1.2 2.8 0.8 2.5 -0.7 -0.9 -0.2 -1.7 0.7 0.1 -2.4 1.4 -0.3 0.5 -1.2 -0.2 -2.0 -1.8 1.0 -0.2 0.8 -1.6 0.0 -1.0 0.7 3.1 0.5 -2.4 0.4 2.5 0.5 -0.3 0.4 0.1 -0.1 -1.0 0.9 0
JH_7 -5.3 -3.7 -0.2 1.6 1.7 6.7 2.7 0.4 0.1 5.1 1.0 3.7 -4.2 -1.7 -3.0 -0.8 -1.9 -0.6 -1.6 2.2 1.1 -1.2 0.9 1.9 1.3 -1.4 0.0 0.6 0.2 -0.4 -1.1 -0.6 0.1 0.1 -0.1 -0.6 0.8 -0.1 0.1 -0.4 0.0 -0.3 -0.1 0
JH_8 -7.1 -1.2 1.0 -2.2 1.3 0.3 -1.3 3.2 0.4 0.6 -0.6 1.2 -1.6 1.5 0.5 -2.9 4.0 2.5 -3.0 -0.2 -1.3 1.9 -3.4 -1.6 -0.4 0.2 -0.6 1.7 -0.7 -0.8 -0.3 0.0 1.5 1.4 0.9 -0.5 -0.2 0.1 -0.3 0.3 1.0 1.0 -0.9 0
JH_9 -7.9 -2.2 2.9 -0.1 5.0 2.7 -0.4 -1.5 -0.3 -0.2 0.7 -2.1 -0.9 3.7 1.1 -2.5 2.1 -0.1 3.0 1.9 -0.1 -2.3 -0.6 1.7 -2.0 0.8 0.9 -0.2 0.0 2.0 1.7 -0.4 -1.5 0.2 1.2 0.7 -0.8 -0.9 -0.3 0.2 -0.5 -0.5 0.3 0
JH_10 -2.7 -2.1 3.8 -5.7 -2.2 4.6 0.8 -0.6 -3.1 1.3 4.4 -0.9 5.2 -2.2 -1.3 3.2 3.5 1.4 0.3 1.5 0.1 2.0 1.7 -1.0 -1.1 0.1 -0.8 -0.1 0.6 -0.2 -0.2 -0.8 0.1 0.0 -0.1 0.1 -0.3 0.3 0.1 -0.2 -0.3 -0.1 0.3 0
JH_11 -3.3 -4.0 5.3 4.6 0.0 3.6 -5.0 -3.2 0.0 -1.3 2.5 -2.3 -0.4 -2.2 0.1 0.3 -1.7 -1.4 -1.7 -4.8 1.8 0.8 -1.4 0.5 -1.1 0.8 1.0 1.3 -0.3 0.4 -0.3 1.3 -0.5 -0.4 -0.6 -0.2 0.2 0.6 0.1 0.7 -0.2 0.3 -0.4 0
JH_12 -6.1 0.1 -1.2 3.2 1.8 2.8 -0.8 -3.6 -4.2 -0.3 -5.0 -1.7 -2.9 0.5 3.1 2.3 2.0 -0.5 1.5 0.3 -1.4 -0.1 1.2 -2.5 1.3 0.3 -0.1 -1.3 2.4 -0.8 -0.7 0.0 1.0 0.0 -1.3 -0.2 0.4 1.0 0.0 0.0 0.2 0.2 -0.3 0

Not centered and scaled

When the data is not centered and scaled, JH dominates on account of it containing more room for variance than the SWS items.

SWS strength
SWS emotion
SWS vulnerable
SWS succeed
SWS care
JH
Subject_Number SWS1 SWS2 SWS3 SWS4 SWS29 SWS35 SWS5 SWS6 SWS7 SWS8 SWS9 SWS10 SWS30 SWS11 SWS12 SWS13 SWS14 SWS15 SWS16 SWS31 SWS17 SWS18 SWS19 SWS20 SWS32 SWS33 SWS21 SWS22 SWS23 SWS24 SWS25 SWS34 JH_1 JH_2 JH_3 JH_4 JH_5 JH_6 JH_7 JH_8 JH_9 JH_10 JH_11 JH_12
1001 4 4 4 4 3 4 3 3 1 3 3 1 3 1 1 1 1 1 2 1 4 4 2 4 2 2 2 2 4 4 2 2 5 4 5 5 5 5 5 5 5 2 1 5
1002 3 3 4 4 1 2 2 2 1 2 2 2 2 3 2 3 3 2 2 3 2 4 1 3 4 4 3 4 3 3 3 4 5 5 4 4 4 4 4 4 2 4 4 4
1003 4 4 3 4 4 4 4 3 2 4 4 4 4 2 3 4 4 4 4 4 2 4 4 4 4 3 4 4 4 4 4 4 3 2 4 4 5 4 4 5 2 4 5 4
1004 4 4 4 4 4 4 4 4 3 3 3 3 4 3 3 4 4 4 4 4 4 4 4 3 4 4 2 1 4 4 4 4 3 4 4 4 4 4 2 4 4 4 4 4
1005 3 3 3 3 2 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 2 2 1 1 4 4 4 4 4 2 4 4 4 4 2 5 4 4 4 5 4 4